Abstract
In this paper, the authors discuss some important sets, including singular sets, exceptional sets, irrational sets, etc., generated by invertible planar piecewise isometric maps. They first extend the coding map onto the entire phase space and characterize singular sets and exceptional sets by the number of codings. Then they reveal the relation among these sets, and show that an irrational set is contained in an exceptional set. And they confirm the existence of admissible rational codings under some conditions (including a necessary and sufficient condition and a sufficient condition). They also discuss dynamical properties of the discontinuity line segments which determine the dynamics of a piecewise isometric system. Finally, they list some open problems for further research.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
